Biostats Ch. 1 & 2

Front 1

Statistics

Back 1

analysis and interpretation of data to objectively evaluate the reliability of conclusions based on the data

Front 2

Goals of Statistics

Back 2

Estimate values of important parameters and test hypotheses about those parameters

(can assess differences between groups and the relationship between variables)

Front 3

Descriptive statistics

Back 3

procedures to summarize/organize data

statistics of location (measure of central tendency, some average value [mean, median, mode])

statistics of dispersion, spread, variability of data (variance, standard deviation)

shape of frequency distribution

Front 4

Inferential statistics

Back 4

enables generalized conclusions from data (using sample data to make statements/conclusions/inferences about whole population)

evaluates two kinds of questions:

1. How reliable are the results (via setting confidence limits to sample stats)

2. How probable is it that the results are due to chance alone? (differences between observed and expected)

Involves hypothesis testing via statistical tests (t-tests, ANOVA, Goodness of Fit) to decide whether or not to reject the underlying null hypothesis

Front 5

Hypothesis testing

Back 5

comparing two or more statistics' values to determine if they are the same or different

Front 6

H0 null hypothesis

Back 6

no difference between the observed and expected

Front 7

Halt alternative hypothesis

Back 7

different between observed and expected

Front 8

variable

Back 8

characteristic that differes among individuals/ smapling units of a population (e.g. length, weight, # of bristles, genotype, N-content, speed)

Front 9

population

Back 9

total set of individuals about which one wishes to draw conclusions (make inferences)

Front 10

sample

Back 10

a collection of observations/measurements (data)

Subset of population (pop. usually too big to sample all)

Front 11

parameter

Back 11

parametric statistic

parametric value for an attribute

true value for the whole population (usually unknown)

Front 12

sample statistic

Back 12

statistic estimate= the value for the attribute calculated from your sample

Population parameters are constants, vs. population estimates will change from one random sample to the next, even though the sample was taken from the same population.

Front 13

variability

Back 13

real world.

sampling will lead to uncertainty (not perfectly representative)

Front 14

sampling error

Back 14

chance difference between a sample estimate and the true parameter for the whole population

large samples= smaller sampling error

Statistics involve the measurement and examination of uncertainty.

statistics become necessary when observations are variable.

Front 15

How closely does sample reflect true values?

Back 15

Poor data (unrepresentative, pseudoreplicated) can lead to erroneous conclusions

Inadequate data (too small sample size) leads to inconclusive results.

Front 16

Statistical considerations can aid in design of experiments to prevent:

Back 16

wrong manner of sampling

too small sample size

unnecessary effort

how you design your experiment will determine the power of different statistical tests

Front 17

Experimental design

Back 17

constructing hypotheses

how to set up experiment

type of data to collect

how to collect data and how much data to collect

goals- to reduce bias and sampling error

Front 18

Bias

Back 18

a systematic discrepancy between estimates and the true population value

Front 19

random sampling

Back 19

minimizes bias and permits sampling error estimate

reliable statistic gives estimate which are close to the true value

Front 20

Stats based on probabalistic distributions which assume

Back 20

random sampling and independence of sampels

Front 21

Different types of sampling

Back 21

Random sampling= best but takes more time (each member of pop has equal and independent chance of being selected)

(random number generator)

Systematic sampling= can be effectively random, much faster, but must make sure no trends are in phase with sampling scheme

Front 22

Inappropriate Sampling

Back 22

Sampling of convenience not likely to be unbiased and independent

Judgment sampling which is always biased

Volunteer bias- volunteers are likely to be different from the average member of the population

Front 23

Numerical variable

Back 23

Quantitative, measurement data

continuous vs discontinuous

measured vs. counted

Front 24

Categorical variable

Nominal

Back 24

Name/describe categories or attributes

qualitative- cannot be measured, not numerical

but you calculate frequencies for each category (either absolute or relative frequencies)

Must use different statistical tests for this type of data

Front 25

Categorical variable

Ranked

Back 25

Ordinal

variable gives information about a data point's rank or order but doesn't tell you exact numerical values of the data points

less information than measurement type but still useful

Mostly categorical (life stages, snake bite severity, size classes, socio-economic categories)

can be numerical rankings but still only know ranking not actual magnitudes of a measurement (numerical score answers on surveys)

Front 26

Independent vs dependent variables

Back 26

try to predict or explain a response variable from an explanatory variable

Front 27

Experimental vs. observational study

Back 27

Experimental- researcher assigns treatments randomly to individuals

Observational- researcher does not assign treatments

Front 28

Accuracy vs. Precision

Back 28

Accuracy- how close to true value

Precision- repeatability (number of digits indicates measurement precision level).

(round to one decimal place more than the original measurements)

Rounding- round up if next decimal place is greater than or equal to five

Front 29

Derived variables

Back 29

calculated from two or more measured variables

ratios, indices, rates, etc.

lose information

may not be normally distributed

Front 30

Frequency distributions

Back 30

distribution of the total number of observations for a variable

shows how often each value of a variable occurs in a sample

absolute frequency- count of how many individuals fit or occur in the category

relative frequency- proportion of total data set represented by each (fraction of occurrences of each value of a variable)

Front 31

Ways to organize data to show distribution

Back 31

list data, frequency table, graph or diagram of frequency distribution

graph (one variable)- curves, bar graphs, and histograms

Front 32

Bar graph

Back 32

categorical and discontinuous numerical data

bars do not touch

Front 33

Histograms

Back 33

Continuous numerical data, grouped into bins

bars do touch

y-axis is frequency density

can't just compare bar heights unless all bars are same width

must calculate area of bar to know absolute frequency

Front 34

Cumulative frequency

Back 34

Sum of all frequencies so far (as move on to higher x values)

Front 35

Dot plots

Back 35

if few data points for discontinuous data or continuous data without a wide range of values

Front 36

Frequency polygon

Back 36

not common

points are places where top of bar would be, then connected with straight lines, don't try to read data between points

Front 37

Steam and leaf display

Back 37

stem- leading digits

leaves- last significant digit (for each data point with that leading digit)

must keep spacing the same between digits

not real graph

freq. distribution with appearance like histogram

ranking, too, so easy to find median,

easy to make and check

does not lose specific information

Front 38

Grouped histograms

Back 38

Comparing numerical variables between groups

Front 39

Grouping of classes

Back 39

Needed when there are too many or too few data pints per x-value

rules of thumb:

10-20 classes usually good, unless small or very large data set

sq. root of n , for total n observations

Sturge's rule

good judgment needed, rather than strict rules

Continuous data- always grouping,

size of interval and where start class intervals can affect appearance of graph

if have too few classes without grouping

for nominal data- can't be helped

for continuous data- need to measure more precisesly

Front 40

Important characteristics of a distribution

Back 40

location- where center is

dispersion- how scattered data are

skewness- symmetrical or not

Front 41

Probability distributions

Back 41

distribution of a variable in the whole population

theoretical probability distributions are often used to approximate the distribution of a variable in the population from which a sample has been drawn

e.g. normal distribution

Front 42

Mosaic plot

Back 42

bar area represents the relative frequency within each group

width of each vertical stack is proportional to the number of observations in that group

Front 43

Two categorical variables

Back 43

Contingency table

grouped bar graph

mosaic plot

Front 44

Two numerical

Back 44

Scatter plot

Line graph

Maps

Front 45

Numerical and categorical

Back 45

box plots

dot plots

multiple histograms

cumulative frequency distributions

Front 46

Guidelines for effective graphs

Back 46

1. make graph elements clear (label axes, include units for measurements, simple font, large text, distinguishable graph symbols, colors easy to see)

2. Show actual data points

3. Make patterns easy to see (avoid chart junk and avoid putting too much info in one graph)(draw figures clearly and minimize clutter)

4. Represent magnitudes honestly (baselines of bar graphs and histograms should be zero)

Front 47

How to make good tables

Back 47

1. Make patterns easy to see (no more digits than necessary, not too much data, arrange to aid pattern detection, list categorical data in natural order if applicable or from highest freq to lowest freq)

2. Represent magnitudes honestly

3. Label clearly